One for all you mathematicians (way beyond my understanding) blog by Paolo Maccallini: "Robert Phair and the trap Many of my readers are probably aware of the attempts that are currently being made to mathematically simulate energy metabolism of ME/CFS patients, integrating metabolic data with genetic data. In particular, dr. Robert Phair has developed a mathematical model of the main metabolic pathways involved in energy conversion, from energy stored in the chemical bonds of big molecules like glucose, fatty acids, and amino acids, to energy stored in adenosine triphosphate (ATP), ready to use. Phair, who is an engineer, determined the differential equations that rule this huge amount of chemical reactions and adapted them to the genetic profile found in ME/CFS patients." https://paolomaccallini.wordpress.com/2018/07/10/me-cfs-a-mathematical-model/

To be honest this model seems too simplistic: It's a relatively easy differential equation for a pretty complex system. I remember in order to model chemical reactions "close to reality" one has to apply quantum mechanics which leads to many-body-systems, which normally are pretty difficult to solve, also numerically. Second I remember the time is the big problem in chemical reactions: the time steps are tiny, somwhere around picoseconds. In the simulations I ran - nano-optics (nonlinear Maxwell's equations) - it simply wasn't possible to choose a discretization step around 10^(-12) (neither in space nor in time, especially not in time). We used the Runge-Kutta-method for time discretization; I remember it was pretty good. But I guess one big problem in this case is to get time t small enough; there's not enough computational power to do that I would say. (We tried using graphical cards because that's faster, but my impression was hard to program.) But who knows...there's so much development. Still, interesting topic; it could be a promising starting point. Overall, I find a simulation approach very promising. I read that Klimas is using this approach. I hope to hear more in that direction.

I think these days there are libraries to use GPUs for computation but generally aimed at machine learning rather than complex sets of differential equations. There are also a few accelerators around but again aimed at machine learning. The increase in processor power has started to tail off but you can use large numbers of cores so if the problem can be divided up (parallelised) into smaller computations then that works well.

Yes. We worked with parallelization, but this only works if your numerical method and your equations enable you to do that. Still, you reach the limits pretty fast for problems that model reality relatively good. (We ran the simulations, the others made the experiments.) I also made simulations for another mathematical problem, and these could be run on the big clusters. Still, one round of simulation took up till a week. I don't know anything about machine learning. I applied numerical methods and implemented them "from scratch" (I used matlab, my colleagues C or even Python, one programmed for graphic cards); there weren't libraries or functions for the stuff we did, except for standard things. I really do wish to see simulations in the ME world. It worked well in nano-optics: simulations -> experiments -> new materials. But I am a bit sceptical if not mathematicians &Co are involved. Numerics can be very tricky, and if you don't stick to rules you can get crap results which you probably don't recognize as such. (Like in meteorology - climate simulations - e.g. where, at least in part, linear models are used )

@Sly Saint Thank you for sharing my blog post! It has been really a pleasure for me to discover this 'old' study and to write about it. We didn't have much mathematical modelling in ME/CFS and I hope there will be a lot more in the future. The link is wrong, the correct one is: https://paolomaccallini.wordpress.com/2018/07/10/me-cfs-a-mathematical-model/ As I wrote in the blog post, the software that they coded is awailable here.